Molecular Dynamics Simulation of Membrane Channels Part III. Nanotubes Theory, Methodology Summer School on Theoretical and Computational Biophysics June 2003, University of Illinois at Urbana-Champaign

Carbon Nanotubes Hydrophobic channels - Perfect Models for Membrane Water Channels A balance between the size and hydrophobicity

Carbon Nanotubes Hydrophobic channels - Perfect Models for Membrane Water Channels Much better statistics No need for membrane and lipid molecules

Carbon Nanotubes Hydrophobic channels - Perfect Models for Membrane Water Channels Much better statistics No need for membrane and lipid molecules

Water Single-files in Carbon Nanotubes Water files form polarized chains in nanotubes

Water-Nanotube Interaction can be Easily Modified Hummer, et. al., Nature, 414: , 2001

Calculation of Diffusion Permeability from MD  0 : number of water molecules crossing the channel from the left to the right in unit time  0 can be directly obtained through equilibrium MD simulation by counting “full permeation events”

carbohydrate 440 nm scattered light H2OH2O carbohydrate + H 2 O lipid vesicles channel-containing proteoliposomes shrinkingreswelling 100 mM Ribitol Liposome Swelling Assay GlpF is an aquaglyecroporin: both water and carbohydrate can be transported by GlpF.

Chemical Potential of Water membrane (2)(1) WW pure water pure water Water flow in either direction is the same, i.e., no net flow of water.

Solutes Decrease the Chemical Potential of Water Semipermeable membrane (2)(1) W+SW pure water dilute solution Water establishes a net flow from compartment (2) to compartment (1). Addition of an impermeable solute to one compartment drives the system out of equilibrium.

Establishment of Osmotic Equilibrium Semipermeable membrane (2)(1) W+SW pure water dilute solution At equilibrium, the chemical potential of any species is the same at every point in the system to which it has access.

Establishment of an Osmotic Equilibrium Semipermeable membrane (2)(1) W+SW pure water dilute solution Solute molar fraction in physiological (dilute) solutions is much smaller than water molar fraction. Osmotic pressure

Establishment of an Osmotic Equilibrium (2)(1) W+SW pure water dilute solution Solute concentration (~0.1M) in physiological (dilute) solutions is much smaller than water concentration (55M).

Osmotic Flow of Water Net flow is zero Volume flux of water Hydraulic permeability Molar flux of water Osmotic permeability (2)(1) W+SW pure water dilute solution

Simulation of osmotic pressure induced water transport may be done by adding salt to one side of the membrane. Semipermeable membrane (1) (2) There is a small problem with this setup! NaCl  Na + +Cl -

Problem: The solvents on the two sides of a membrane in a conventional periodic system are connected. (1) (2) (1) (2) (1) (2) (1) (2) (1) (2) (1) (2) (1) (2) (1) (2) (1) (2)

We can include more layers of membrane and water to create two compartment of water that are not in contact (2) (1) Semipermeable membrane Semipermeable membrane NaCl

Semipermeable membrane Semipermeable membrane (2) (1) NaCl U N I T C E L L

The overall translation of the system is prevented by applying constraints or counter forces to the membrane. membrane water Realizing a Pressure Difference in a Periodic System f is the force on each water molecule, for n water molecules Fangqiang Zhu F. Zhu, et al., Biophys. J. 83, 154 (2002).

Applying a Pressure Difference Across the Membrane Applying force on all water molecules. Not a good idea!

Applying a Pressure Difference Across the Membrane Applying force on bulk water only. Very good

Applying a Pressure Difference Across the Membrane Applying force only on a slab of water in bulk. Excellent P f can be calculated from these simulations

Calculation of osmotic permeability of water channels p f : 7.0 ± 0.9  cm 3 /s Exp: 5.4 – 11.7  cm 3 /s p f : 1.4  cm 3 /s GlpF Aquaporin-1

stereoisomers Stereoselective Transport of Carbohydrates by GlpF Some stereoisomers show over tenfold difference in conductivity.

GlpF + glycerol GlpF + water Channel Constriction HOLE2: O. Smart et al., 1995 red < 2.3 Å 2.3 Å > green > 3.5 Å blue > 3.5 Å

Selectivity filter

Interactive Molecular Dynamics VMD NAMD

Observed Induced Fit in Filter

Confinement in Filter Selection occurs in most constrained region. Caused by the locking mechanism. RMS motion in x and y z (Å) Filter region

Ribitol Optimal hydrogen bonding and hydrophobic matching Arabitol 10 times slower Evidence for Stereoselectivity

Dipole Reversal in Channel Dipole reversal pattern matches water. Selects large molecules with flexible dipole. cos(dipole angle with z) z (Å) Dipole reversal region